The finite-time tracking control problem of rigid manipulator system with mismatched disturbances is investigated via a composite control method. The proposed composite controller is based on finite-time disturbance observer and adding a power integrator technique. First, a finite-time disturbance observer is designed which guarantees that the disturbances can be estimated in a finite time. Then, a composite controller is developed based on adding a power integrator approach and the estimates of the disturbances. Under the proposed composite controller, the manipulator position can track the desired position in a finite time. Simulation results show the effectiveness of the proposed control scheme.
Due to some superior capacities, such as high accuracy, high stiffness, and high load-carrying [
From the point view of convergence rates, most of the existing results on control of rigid manipulators achieve asymptotic stability results for the closed-loop systems [
Note that the aforementioned control schemes for manipulators with disturbances work in a robust way, which implies that the disturbances attenuation is at the price of sacrificing their nominal control performances. To improve this problem, a feasible way is to use feedforward-feedback composite control rather than pure feedback control to solve the control problems of manipulators with disturbances. Disturbance observer based control (DOBC) is an effective composite control method, which is composed of disturbance observer (DO) design and nominal feedback controller design [
In this paper, a composite control scheme is developed for manipulator systems with mismatched disturbances. The composite control algorithm is designed based on finite-time disturbance observer (FTDO) and adding a power integrator control method. Under the proposed composite controller, in the presence of mismatched disturbances, the manipulator position can track the desired position in a finite time.
The remainder of this paper is organized as follows. Section
Consider the following nonlinear autonomous system:
The equilibrium
Considering system ( There exist real numbers
Then the origin is a finite-time stable equilibrium of system (
Let
For any real numbers
The dynamics of a
Let
Controller design is mainly composed of two parts, that is, disturbance observer design and composite controller design.
In practice, lots of disturbances satisfy Assumption
Under Assumption
By letting
Assume that the desired position vector
Defining the tracking errors as
The stability analysis can be divided into two steps. In Step
Under the condition without disturbance observer, with adding a power integrator method, a controller for manipulator system (
Simulations are conducted on a two-link rigid robot manipulator. The cases without/with output noises are considered in the simulations. The manipulator model is shown in Figure
The two-link robot manipulator model.
To validate the effectiveness of the proposed composite control algorithm, closed-loop system performances under composite controller (
Taking the practical input saturation into consideration, the control inputs for both controller (
Simulation results are presented in Figures
Disturbance observation errors of the 1st link. (a) Observation error of
Disturbance observation errors of the 2nd link. (a) Observation error of
Response curves of system (
In this part, in the presence of output measurement noises, the closed-loop system performances under composite controller (
Generally speaking, in practice, higher-frequency measurement noises can be filtered by some filters, for example, Kalman filters. In this way, the measured states used by the controllers are usually signals with only lower-frequency noises. Hence, in simulations, only lower-frequency noises are considered and the output measurement noises are assumed to be
Simulation results are given in Figures
Disturbance observation errors of the 1st link in the presence of output measurement noises. (a) Observation error of
Disturbance observation errors of the 2nd link in the presence of output measurement noises. (a) Observation error of
Response curves of system (
This paper has studied the position tracking control problem of rigid manipulator system with mismatched disturbances. By using adding a power integrator technique and FTDO method, a composite control scheme has been developed. The proposed control method has realized that the manipulator positions tracked the desired positions in finite time and simulations have shown the effectiveness of the proposed composite control algorithm.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by the National Natural Science Foundation of China under Grants 61473080 and 61503078, the Natural Science Foundation of Jiangsu Province under Grant BK20150626, China Postdoctoral Science Foundation Funded Project under Grant 2015M570398, the Fundamental Research Funds for the Central Universities under Grant 2242015K40029, and the Priority Academic Program Development of Jiangsu Higher Education Institutions.